Simultaneous stopping or tripping of DG in bulk power system might result in widespread and severe voltage problems by load instability. The stability cannot be explained by P-V curves only, because load characteristic is dynamic. In order to solve voltage problems in bulk power system, it is important to understand the mechanism of load instability and use accurate models of lower voltage subsystems (such as subtransmission and distribution system).For analyzing load stability without detailed simulation, this paper presents torque-speed characteristic curves of induction motor considering power system condition and constant impedance load. A parallel composite of constant impedance and induction motor (IM) is adopted as dynamic load model shown in Fig. 1. The electrical torque-speed characteristic curves of IM is drawn by using Eqs. (1) and (2).The mechanical torque is in proportion to n-th power of the speed (e.g. 2nd in Fig. 2). These curves have three intersections of electrical power input and mechanical power output in the case of IM Fig. 1. 1-load to the infinite bus model considering dynamic load Fig. 2. Torque-speed curve of induction motor considering power system and constant Z load 45% proportion (see Fig. 2(a)). In this case, the steady state α might move to the stalled state γ through the unstable state β by a disturbance. On the other hand, it has only one intersection in the case of IM 35% (see Fig. 2(b)). Even if the system has a severe disturbance, it can recover the steady state α. These studies explain that the condition with one intersection is stable, and the condition with three intersections might be unstable by a disturbance (see Fig. 3(a)(b)).As the results of examining the curves in various conditions, this paper also presents some cautions for bulk power system modeling with DG. The studies make it clear that model order reduction and load dropping out are important concerns.A bulk power system model whose lower voltage subsystems are reduced by an accurate model is introduced in order to check out the problems by DG-stopping. As to the numerical simulation, a great amount of DG-stopping leads to voltage instability in bulk power system (see Fig. 4(a)), and it is greatly improved by DG-voltage regulation (see Fig. 4(b)).Load instability will be more serious problem of power system with high DG penetration. It is desired to grasp the risk and take measures to meet the situation in advance.
SUMMARYTransient stability may be seriously affected when a large number of distributed generators (DG) stop simultaneously during voltage sag. It is necessary to analyze accurately the dynamics of bulk power systems with high DG penetration. In this paper, transient stability is studied by analyzing power-angle curves of generators while considering load dynamics and model order reduction at lower voltages. Based on the analysis, a decrease in the load internal resistance after voltage sag causes transient instability of generators. The phenomenon is confirmed through simulation using a one-machine and one-load model. This paper also suggests that the simulation results might be misled by traditional bulk power system modeling such as using the static load model and ignoring impedance at lower voltages. As for the numerical simulation, a large level of DG stoppage leads to transient step out in a bulk power system, and the stability is greatly improved by DG voltage regulation.
It is well known that adequate dynamic load model is essential for evaluating power system stability. The simulation results using traditional static load models are sometimes misleading especially in short-term synchronous and voltage stability, because those models neglect dynamic behavior of existing loads. Some load models based on physical structure have been studied. One example of them is the composite load model made of parallel constant admittance and induction motor (IM). However there are two difficulties. One is determining various parameters. Another is the measurement of series reactance from observation point to internal load.For representing the behavior of actual load, this paper presents a concept of dynamic load, that is, a variable conductance G behind a constant series reactance X (see Fig. 1). The variable conductance G means the field of energy conversion from electricity to the others. Magnitude of G varies according to the conditions of load and power system. The constant susceptance Bc means the sum of load excitation reactances and compensation capacitors aggregated to the observation point approximately.This paper also presents a method for determining the reactance X by using measured data. Equation (1) shows the relationship of measured variables and model parameters. By assuming an adequate fixed value of Bc, X remains almost constant (about 25% in load MW base), but G takes much higher value instantaneous after fault clearing (see Fig. 2). The tendency is commonly seen in all of 64 measured data in major disturbances, and agrees with the concept. As to the numerical simulation, the behavior of existing loads after instantaneous voltage sag is well represented by a parallel composite of a constant admittance and an induction motor behind a series reactance on the CRIEPI-Y-method, which is a typical simulation tool for power system analysis. An example is shown in Fig. 3. Using parameters of IM assumed as the standard values investigated by CRIEPI in the past, IM load factor 0.5, and proportion of IM 40% to 70%, all the 64 simulation results proved to agree with their measured data well. Also the proportion of IM agrees with the static power-voltage sensitivity factor (0.7 to 1.3). It reinforces the concept and the method. On the other hand, traditional static load model cannot explain load's dynamic behavior (see Fig. 4).Dynamic load model will be more essential in metamorphosing power system by such as retirement of aged thermal generation and penetration of distributed generation, and so on.
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